Large Language Models (LLMs), such as ChatGPT, have recently been applied to various NLP tasks due to its open-domain generation capabilities. However, there are two issues with applying LLMs to dialogue tasks. 1. During the dialogue process, users may have implicit intentions that might be overlooked by LLMs. Consequently, generated responses couldn't align with the user's intentions. 2. It is unlikely for LLMs to encompass all fields comprehensively. In certain specific domains, their knowledge may be incomplete, and LLMs cannot update the latest knowledge in real-time. To tackle these issues, we propose a framework~\emph{using LLM to \textbf{E}nhance dialogue response generation by asking questions to \textbf{D}etect user's \textbf{I}mplicit in\textbf{T}entions} (\textbf{EDIT}). Firstly, EDIT generates open questions related to the dialogue context as the potential user's intention; Then, EDIT answers those questions by interacting with LLMs and searching in domain-specific knowledge bases respectively, and use LLMs to choose the proper answers to questions as extra knowledge; Finally, EDIT enhances response generation by explicitly integrating those extra knowledge. Besides, previous question generation works only focus on asking questions with answers in context. In order to ask open questions, we construct a Context-Open-Question (COQ) dataset. On two task-oriented dialogue tasks (Wizard of Wikipedia and Holl-E), EDIT outperformed other LLMs.